Distribution of geometric sequences modulo 1
type: Item
instance of: scholarly article
title: Distribution of geometric sequences modulo 1
zbMATH Open document ID: 1177.11060
author: Hajime Kaneko
published in: Results in Mathematics
publication date: 2008-09-04T00:00:00Z
review text: The main result of this paper is a lower bound for \(\limsup_{n\to \infty}\| B\alpha^n \|\) where \(B\) is a real number and \(\alpha\) is an algebraic irrational number. The author also proved that for a fixed real number \(C\) and arbitrary positive numbers \(\delta\) and \(M\), the set of \(\alpha >M\) satisfying \(\limsup_{n\to \infty} \| C\alpha^n \| \leq \frac{1+\delta}{2\alpha}\) is at least countable and satisfying \(\limsup_{n\to \infty} \| C\alpha^n \| \leq \frac{1+\delta}{\alpha}\) is at least uncountable.
reviewed by: Jaroslav Hančl
Mathematics Subject Classification ID: 11J71
Mathematics Subject Classification ID: 11R06
Mathematics Subject Classification ID: 11B85
zbMATH DE Number: 5320906
zbMATH Keywords: distribution
zbMATH Keywords: algebraic numbers
zbMATH Keywords: geometric progression
MaRDI profile type: Publication
full work available at URL: s00025-008-0287-3
OpenAlex ID: W2074819691
DOI: 10.1007/S00025-008-0287-3
description: scientific article; zbMATH DE number 5320906